SOLUTION: Evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 and 1, and at x=1. Show your work. Use the resulting ordered p

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 and 1, and at x=1. Show your work. Use the resulting ordered p      Log On


   

Question 251254: Evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 and 1, and at x=1. Show your work. Use the resulting ordered pairs to plot the graph; submit the graph via the Dropbox. State the equation of the line asymptotic to the graph (if any).
y = log4 (x) + 4
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+log%284%2C+%28x%29%29+%2B+4
Since the logarithm is base 4 ans since no calculator I know can find base 4 logarithms, it will help tremendously if we choose our x values wisely. We want to choose x's that are powers of 4! For the three x's greater than 1: 4, 16 and 64 (since 4+=+4%5E1, 16+=+4%5E2 and 64+=+4%5E3). For the x's between 0 an 1: 1/4, 1/16 and 1/64 (since 1%2F4+=+4%5E%28-1%29, 1%2F16+=+4%5E%28-2%29 and 1%2F64+=+4%5E%28-3%29. And even x = 1 is a power of 4 since 1+=+4%5E0!

Using these x's we get:
x = 4: y+=+log%284%2C+%284%29%29+%2B+4+=+1+%2B+4+=+5
x = 16: y+=+log%284%2C+%2816%29%29+%2B+4+=+2+%2B+4+=+6
x = 64: y+=+log%284%2C+%2864%29%29+%2B+4+=+3+%2B+4+=+7
x = 1/4: y+=+log%284%2C+%281%2F4%29%29+%2B+4+=+-1+%2B+4+=+3
x = 1/16: y+=+log%284%2C+%281%2F16%29%29+%2B+4+=+-2+%2B+4+=+2
x = 1/64: y+=+log%284%2C+%281%2F64%29%29+%2B+4+=+-3+%2B+4+=+1
x = 1: y+=+log%284%2C+%281%29%29+%2B+4+=+0+%2B+4+=+4
We now have 7 points to plot.

The asymptotes for a logarithmic equation will be vertical asymptotes at values for x that make an argument of a logarithm zero, if any. We have just one logarithm so we find the asymptotes, if any, by setting the argument equal to zero and solving:
x = 0
(Not much solving to do here!) There is a vertical asymptote at x = 0 (aka the y-axis).